# Natural Earth projection

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The natural Earth projection is a pseudocylindrical map projection designed by Tom Patterson and introduced in 2012. It is neither conformal nor equal-area.

## Contents

It was designed in Flex Projector, a specialized software application that offers a graphical approach for the creation of new projections. [1] [2]

## Definition

The natural Earth is defined by the following formulas:

{\displaystyle {\begin{aligned}x&=0.8707\times l(\varphi )\times \lambda ,\\y&=0.8707\times 0.52\times d(\varphi )\times \pi ,\end{aligned}}},

where

• x, y are the Cartesian coordinates;
• λ is the longitude from the central meridian;
• φ is the latitude;
• l(φ) is the length of the parallel at latitude φ;
• d(φ) is the distance of the parallel from the equator at latitude φ.

l(φ) and d(φ) are given as polynomials, initially from interpolation of the following values in Flex Projector [3] :

φ (degrees)l(φ)d(φ)
01.00000.0000
50.99880.0620
100.99530.1240
150.98940.1860
200.98110.2480
250.97030.3100
300.95700.3720
350.94090.4340
400.92220.4958
450.90060.5571
500.87630.6176
550.84920.6769
600.81960.7346
650.78740.7903
700.75250.8435
750.71600.8936
800.67540.9394
850.62700.9761
900.56301.0000

The values for the southern hemisphere are calculated by changing the sign of the corresponding values for the northern hemisphere.

## Related Research Articles

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## References

1. Šavrič, Bojan; Jenny, Bernhard; Patterson, Tom; Petrovič, Dušan; Hurni, Lorenz (February 17, 2012). "A Polynomial Equation for the Natural Earth Projection" (PDF). Oregon State University. Archived from the original (PDF) on 2016-03-03. Retrieved January 24, 2020.
2. Jenny, Bernhard; Patterson, Tom; Hurni, Lorenz (2008). "Flex Projector–Interactive Software for Designing World Map Projections". Cartographic perspectives. Retrieved January 24, 2020.
3. "Natural Earth Projection: Home". www.shadedrelief.com. Archived from the original on 2012-04-07. Retrieved 2017-02-12. It was originally designed in Flex Projector using graphical methods and now exists as a polynomial version.